Decision Analysis

1. Chapter 16 Decision Analysis

2. Introduction • The focus of previous chapters: • Decision-making when consequences of alternative decisions are known with a reasonable degree of certainty • Testing (experimentation) can reduce level of uncertainty • Decision analysis • Addresses decision-making in the face of great uncertainty • Provides framework and methodology

3. 16.1 A Prototype Example • Goferbroke Company owns land that may contain oil • Geologist reports 25% chance of oil • Another company offers to purchase land for $90k • Goferbroke option: drill for oil at cost of $100k • Potential gross profit $800k (net $700k) • Potential net loss of $100k if land is dry • Need to decide whether to drill or sell

4. A Prototype Example

5. 16.2 Decision Making Without Experimentation • Decision maker must choose an alternative • From a set of feasible alternatives • State of nature • Factors in place at the time of the decision that affect the outcome • Payoff table shows payoff for each combination of decision alternative and state of nature

6. Decision Making Without Experimentation • Analogy with game theory • Decision maker is player 1 • Chooses one of the decision alternatives • Nature is player 2 • Chooses one of the possible states of nature • Each combination of decision and state of nature results in a payoff • Payoff table should be used to find an optimal alternative for the decision maker • According to an appropriate criterion

7. Decision Making Without Experimentation • Differences from game theory • Nature is not rational or self-promoting • Decision maker likely has information about relative likelihood of possible states of nature • Probability distribution: prior distribution • Probabilities: prior probabilities

8. Decision Making Without Experimentation • Formulation of the prototype example • The maximin payoff criterion • Extremely conservative in nature • Assumes nature is a malevolent opponent

9. Decision Making Without Experimentation • The maximum likelihood criterion • Identify the most likely state of nature • Choose the decision alternative with the maximum payoff for this state of nature • In the example: the decision would be to sell, since the most likely state of nature is dry • Does not permit gambling on a low-probability, big payoff

10. Decision Making Without Experimentation • Bayes’ decision rule • Commonly used • Using the best available estimates of the probabilities of the states of nature, calculate the payoff value for each decision alternative • Choose the alternative with the maximum expected payoff value • Alternative selected: drill for oil

11. Decision Making Without Experimentation • Sensitivity analysis with Bayes’ decision rule • Assume prior probability of oil, p, is between 15 and 35 percent • Figure 16.1 shows plot of expected payoff versus p • Crossover point • Point at which decision shifts from one alternative to another

13. 16.3 Decision Making With Experimentation • Additional testing (experimentation) • Frequently used to improve preliminary probability estimates • Improved estimates: posterior probabilities • Continuing with oil drilling example • Seismic survey can refine the probability • Cost of survey is $30,000

14. Decision Making With Experimentation • Possible survey findings • USS: unfavorable seismic soundings • Indicates oil is unlikely • FSS: favorable seismic soundings • Indicates oil is likely • Based on past experience with seismic soundings:

15. Decision Making With Experimentation • Bayes’ theorem

16. Decision Making With Experimentation • If seismic survey finding is USS: • If finding is FSS:

17. Decision Making With Experimentation

18. Decision Making With Experimentation • Is it worth it to undertake the cost of the survey? • Need to determine potential value of the information

19. Decision Making With Experimentation • Expected value of perfect information • Provides an upper bound on the potential value of the experiment • If upper bound is less than experiment cost: • Forgo the experiment • If upper bound is higher than experiment cost: • Calculate the actual improvement in the expected payoff • Compare this improvement with experiment cost

20. Decision Making With Experimentation

21. Decision Making With Experimentation • Expected value of experimentation (EVE) • The difference between the expected payoff with experimentation and the expected payoff without experimentation • For the Goforbroke Co. • Since this exceeds the experiment cost, the experiment should be done

22. 16.4 Decision Trees • Functions: • Visually displaying a problem • Organizing computational work • Especially helpful when a sequence of decisions must be made • Constructing the decision tree • Should a seismic survey be conducted before a decision is chosen? • Which action (drill for oil or sell land) should be chosen?

23. Decision Trees • Nodes (forks) • Junction points in the tree • Branches • Lines in the decision tree • Decision node • Indicated by a square • Indicates decision needs to be made at that point

24. Decision Trees • Event node (chance node) • Indicates random event occurring at that point • Note expected payoff over its decision node • Indicate chosen alternative • Insert a double dash as a barrier through each rejected branch • Backward induction procedure • Leads to optimal policy

28. 16.5 Using Spreadsheets to Perform Sensitivity Analysis • Create a decision tree using ASPE • Select Add Node from the Decision Tree/Node menu

29. Using Spreadsheets to Perform Sensitivity Analysis • Full decision tree shown in Figure 16.11 • Expand the spreadsheet for performing sensitivity analysis • Consolidate the data and result on the right hand side • Advantage: need to only change data in one place • Approaches • Select new trial values • Consider a range of values

31. 16.6 Utility Theory • Monetary values may not always correctly represent consequences of taking an action • Utility functions for money U(M) • People may have an increasing or decreasing marginal utility for money • Decision maker is indifferent between two courses of action if they have the same utility

32. Utility Theory • Equivalent lottery method for determining utilities • See Page 710 in the text • Applying utility theory to the full Goforbroke Co. problem • Identify the utilities for all the possible monetary payoffs • Shown in Table 16.7 on next slide

33. Utility Theory • Exponential utility function • Another approach for estimating U(M) • Involves an individual’s risk tolerance, R

34. 16.7 The Practical Application of Decision Analysis • Real applications involve many more decisions and states of nature: • Than were considered in the prototype example • Decision trees would become large and unwieldy • Several software packages are available • Algebraic techniques being developed and incorporated into computer solvers

35. The Practical Application of Decision Analysis • Other graphical techniques • Tornado charts • Influence diagrams • Decision conferencing • Technique for group decision making • Group of people work with a facilitator • Analyst builds and solves models on the spot • Consulting firm may be used if company does not have analyst trained in OR techniques

36. 16.8 Conclusions • Decision analysis is an important technique when facing decisions with considerable uncertainty • Decision analysis involves: • Enumerating potential alternatives • Identifying payoffs for all possible outcomes • Quantifying probabilities for random events • Decision trees and utility theory are tools for decision analysis